Physics 114
AC Circuits. Oscilloscope
Alvaro Alvarez
Partner: Shaine Powers
Group 1
Ta: Salman
4/1/14
Abstract:
In the experiment AC Circuits. Oscilloscope, the main objective was to use a signal generator (SG) to create a sine wae and using an oscilloscope we had to bserve the various components of a sine waves and there relationships; the component RMS, amplitude, period and frequency. Another objective was to use the RLC circuit to determine the resonant frequency. In order to complete these ojectives the circuit was first set up as in figure 1 and RMS, period, frequency and amplitude were calculated and measured. The experimental amplitude was 0.875Vac, the frequency was 1001Hz, and the period was one second. The difference beween the theoretical frequcy from the signal generator was compared to the experimental frequency giving a 0.1% error. For the second part of the lab the RLC circuit was set up (figure 2) and from there the resonant frequency was found for this was done three times (table 1). After this the voltage drop was measured in the range of 800-300Hz; the different frequencies withc corresponding average power that dissipated in the resistor was inputted into GA (table 2,). From there the power vs frequency graph was plotted. and finally the theoretical angular frequency 1.0846 x 104rad/sec was compared to the experimentally found frequency of 1.0820 x 104rad/sec, giving a 0.24% error.

Objective:
In experiment number nine “AC Circuits. Oscilloscope” The main objective in the experiment was to use a signal generator to produce an AC signal and determine the relationship between the rms value and the amplitude of the voltage of the wave and also the period and the frequency of the signal. A secondary objective was to use an RLC circuit and determine both the resonant frequency and the dissipated power of the main resistor.

Procedure:
For part one of the experiment the circuit was built as in (figure 1), after the circuit was assembled the signal generator (SG), was set to 1000Hz.on the scope the SEC/DIV control was set to one complete period of the measured waveform. After this the period T of the wave was measured and the frequency was calculated and compared to the SG. After this the scope is set to decoupling and the DC offset is set at ~ 1.0V. The DMM was set to DC and the voltage reading was compared to the SR reading. Last part for part one was to set the DC offset back to zero , change the DMM to Ac and from that determines the amplitude of the scope which was finally compared to the reading of the DMM.

For part two of the lab the first step was to set up the RLC circuit as in (figure 2) and make sure that all the setting were correct. From there the resonant frequency was found for when the resistor has max current; this was done three times (table 1). After this the voltage drop for the resistor was done in the range of 800-300Hz; from the different frequencies the average power that dissipated in the resistor was calculated (table 2, column 1). From there the power vs frequency graph was plotted. From the data the experimental angular frequency was calculated and compared to the actual value of the angular frequency.

Data and Calculations:
Table 1: Three independent measurement of the resonant frequency Trial | Frequency (Hz) | Vac dissipated (v) | 1 | 1749 | 0.6888 | 2 | 1754 | 0.687 | 3 | 1725 | 0.685 |
Part 1:
Signal generator output: 1000Hz
Period (T) Experimental= 1ms
Frequency: ( 1/T)
Theoretical:
1/(.2m/s)(5boxes)=1 KHz.
Experimental: 1001 Hz
Scope analysis after pulling offset:
A 2 box drop (1 sec)= 1Vdrop
Amplitude of sine wave:
V0= Vpp/2
V0= ((3.5)(0.5)/(2))
Experimental :V0= 0.875Vac
Percent error for Frequency %error =( |theo-exp| / theo )*100 = (|1000Hz-1001Hz|/1000Hz)*100 =0.1%
Part 2:
Theoretical W:
=1/sqrt(LC)
=1/sqrt((.085)(0.1uF) =1.0846 x 104rad/sec
Experimental W (graph , a value)
=1.0820 x 104rad/sec

Percent error for Angular Frequncy:
%error =( |theo-exp| / theo )*100 = (|1.0846-1.0820|/1.0846Hz)*100 =0.24%
ERROR:
∆WW=12∆LL+ ∆CC=12.10+.10=10.0%

Discussion:
In the lab physics of AC Circuits. Oscilloscope the results for part one showed that the period for the sine wave created by the SG was 1ms, the voltage of the amplitude of the wave was 0.875Vac, and the frequency was approximately 1001Hz which if compared to the theoretical frequency of 1000Hz gives a 0.1% discrepancy. For part two of the experiment the results showed a theoretical angular frequency of 1.0846 x 104rad/sec which if compared to the experimental angular frequency collected from (graph 1) was 1.0820 x 104rad/sec this gives a very small percent error of 0.24%. From this data we can conclude that the period of a waveform is the time required for one complete cycle of the wave to occur so we get a relationship of Tperiod=1/F. Furthermore the rms value of a waveform represents the squaring of the amplitude at each point of a waveform and then taking its mathematical average; this is done because if you try to just take the ad amplitude of a sine wave would just equal zero due o it going from positive to negative. Also by analyzing table 2 and graph 1 we can see a relationship between power and angular frequency. As power increases angular frequency increases up to a certain threshold which then start to go down and power increases; this power threshold ~0.002W on graph 1. Also by looking at graph one we can see that the resistance in the circuit increased this is most likely due to the cable adding resistance. This lab had extremely minimal percent error <1% and so we can conclude that the lab was done properly.
Conclusion:
After completing this lab we can conclude that we correctly completed the lab with very little to no error. In this lab we were able to meet all the objectives and now have a much better understanding of the relationships between different components of the sine wave generated by the SG. For example we can see that for a sine wave as power increases angular frequency will correspondingly increase as well until it reaches a certain threshold and will then begin to decrease (graph 1). This same relationship can be seen for frequency and Voltage (Vac) on table 1.